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Definition 2 Let X and Y be random variables with their expectations µ X = E(X) and µ Y = E(Y), and k be a positive integer 1 The kth moment of X is defined as E(Xk) If k = 1, it equals the expectation 2 The kth central moment of X is defined as E(X − µ X)k If k = 2, then it is called the variance of X and is denoted by var(X).

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∂µ2 = −µ−2 i=1 x i < 0 Thus there is a local maximum at µ = ¯x We then note that as µ → 0 or µ → ∞, the loglikelihood ‘(µ;x) approaches −∞ Thus µ = ¯x is a global maximum, and the maximum likelihood estimate of µ is ˆµ = ¯x The maximum likelihood estimator in this example is then ˆµ(X) = X¯ Since µ is the. MetamorphosisW ÌW ÌBOOKMOBIÙl °)` 1– ¦ C K¹ T„ x f4 o wò €˜ ‰) ‘¾ š £;. €(耴10"âgcolor="#f5f7f8€ orde€ˆ1 blockquote ׂ 0‚‡‚€align="leftƒ@tt>construction €ˆ‚¸ived basedo_init€’ €¯ 9appel ñ 9ápresìa ‚ç‚ãl'objet‚ä‚W‚ü/„‘ˆ „éˆK/†çˆçˆçˆà‰ p‰Ž4"÷idth‰Û‡¼justify‰w‰p ?">Onòevient à îotreôableauóurì€xypˆðynamique†àura xŒÀsä'un€™Š_ (ˆ pŠ Šö)  †Ÿ.

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